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The catalytic transformation of C-H to C-N bonds offers rapid access to fine chemicals and high-performance materials, but achieving high selectivity from undirected aminations of unactivated C(sp3)-H bonds remains an outstanding challenge. We report the origins of the reactivity and selectivity of a Cu-catalyzed C-H amidation of simple alkanes. Using a combination of experimental and computational mechanistic studies and energy decomposition techniques, we uncover a switch in mechanism from inner-sphere to outer-sphere coupling between alkyl radicals and the active Cu(II) catalyst with increasing substitution of the alkyl radical. The combination of computational predictions and detailed experimental validation shows that simultaneous minimization of both Cu-C covalency and alkyl radical size increases the rate of reductive elimination and that both strongly electron-donating and electron-withdrawing substituents on the catalyst accelerate the selectivity-determining C-N bond formation process as a result of a change in mechanism. These findings offer design principles for the development of improved catalyst scaffolds for radical C-H functionalization reactions.
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The chemical bond is the cornerstone of chemistry, providing a conceptual framework to understand and predict the behavior of molecules in complex systems. However, the fundamental origin of chemical bonding remains controversial and has been responsible for fierce debate over the past century. Here, we present a unified theory of bonding, using a separation of electron delocalization effects from orbital relaxation to identify three mechanisms [node-induced confinement (typically associated with Pauli repulsion, though more general), orbital contraction, and polarization] that each modulate kinetic energy during bond formation. Through analysis of a series of archetypal bonds, we show that an exquisite balance of energy-lowering delocalizing and localizing effects are dictated simply by atomic electron configurations, nodal structure, and electronegativities. The utility of this unified bonding theory is demonstrated by its application to explain observed trends in bond strengths throughout the periodic table, including main group and transition metal elements.
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Excitation of iron pentacarbonyl [Fe(CO)5], a prototypical photocatalyst, at 266 nm causes the sequential loss of two CO ligands in the gas phase, creating catalytically active, unsaturated iron carbonyls. Despite numerous studies, major aspects of its ultrafast photochemistry remain unresolved because the early excited-state dynamics have so far eluded spectroscopic observation. This has led to the long-held assumption that ultrafast dissociation of gas-phase Fe(CO)5 proceeds exclusively on the singlet manifold. Herein, we present a combined experimental-theoretical study employing ultrafast extreme ultraviolet transient absorption spectroscopy near the Fe M2,3-edge, which features spectral evolution on 100 fs and 3 ps time scales, alongside high-level electronic structure theory, which enables characterization of the molecular geometries and electronic states involved in the ultrafast photodissociation of Fe(CO)5. We assign the 100 fs evolution to spectroscopic signatures associated with intertwined structural and electronic dynamics on the singlet metal-centered states during the first CO loss and the 3 ps evolution to the competing dissociation of Fe(CO)4 along the lowest singlet and triplet surfaces to form Fe(CO)3. Calculations of transient spectra in both singlet and triplet states as well as spin-orbit coupling constants along key structural pathways provide evidence for intersystem crossing to the triplet ground state of Fe(CO)4. Thus, our work presents the first spectroscopic detection of transient excited states during ultrafast photodissociation of gas-phase Fe(CO)5 and challenges the long-standing assumption that triplet states do not play a role in the ultrafast dynamics.
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Porous solids can accommodate and release molecular hydrogen readily, making them attractive for minimizing the energy requirements for hydrogen storage relative to physical storage systems. However, H2 adsorption enthalpies in such materials are generally weak (-3 to -7 kJ/mol), lowering capacities at ambient temperature. Metal-organic frameworks with well-defined structures and synthetic modularity could allow for tuning adsorbent-H2 interactions for ambient-temperature storage. Recently, Cu2.2Zn2.8Cl1.8(btdd)3 (H2btdd = bis(1H-1,2,3-triazolo-[4,5-b],[4',5'-i])dibenzo[1,4]dioxin; CuI-MFU-4l) was reported to show a large H2 adsorption enthalpy of -32 kJ/mol owing to π-backbonding from CuI to H2, exceeding the optimal binding strength for ambient-temperature storage (-15 to -25 kJ/mol). Toward realizing optimal H2 binding, we sought to modulate the π-backbonding interactions by tuning the pyramidal geometry of the trigonal CuI sites. A series of isostructural frameworks, Cu2.7M2.3X1.3(btdd)3 (M = Mn, Cd; X = Cl, I; CuIM-MFU-4l), was synthesized through postsynthetic modification of the corresponding materials M5X4(btdd)3 (M = Mn, Cd; X = CH3CO2, I). This strategy adjusts the H2 adsorption enthalpy at the CuI sites according to the ionic radius of the central metal ion of the pentanuclear cluster node, leading to -33 kJ/mol for M = ZnII (0.74 Å), -27 kJ/mol for M = MnII (0.83 Å), and -23 kJ/mol for M = CdII (0.95 Å). Thus, CuICd-MFU-4l provides a second, more stable example of optimal H2 binding energy for ambient-temperature storage among reported metal-organic frameworks. Structural, computational, and spectroscopic studies indicate that a larger central metal planarizes trigonal CuI sites, weakening the π-backbonding to H2.
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High or enriched-purity O2 is used in numerous industries and is predominantly produced from the cryogenic distillation of air, an extremely capital- and energy-intensive process. There is significant interest in the development of new approaches for O2-selective air separations, including the use of metal-organic frameworks featuring coordinatively unsaturated metal sites that can selectively bind O2 over N2 via electron transfer. However, most of these materials exhibit appreciable and/or reversible O2 uptake only at low temperatures, and their open metal sites are also potential strong binding sites for the water present in air. Here, we study the framework CuI-MFU-4l (CuxZn5-xCl4-x(btdd)3; H2btdd = bis(1H-1,2,3-triazolo[4,5-b],[4',5'-i])dibenzo[1,4]dioxin), which binds O2 reversibly at ambient temperature. We develop an optimized synthesis for the material to access a high density of trigonal pyramidal CuI sites, and we show that this material reversibly captures O2 from air at 25 °C, even in the presence of water. When exposed to air up to 100% relative humidity, CuI-MFU-4l retains a constant O2 capacity over the course of repeated cycling under dynamic breakthrough conditions. While this material simultaneously adsorbs N2, differences in O2 and N2 desorption kinetics allow for the isolation of high-purity O2 (>99%) under relatively mild regeneration conditions. Spectroscopic, magnetic, and computational analyses reveal that O2 binds to the copper(I) sites to form copper(II)-superoxide moieties that exhibit temperature-dependent side-on and end-on binding modes. Overall, these results suggest that CuI-MFU-4l is a promising material for the separation of O2 from ambient air, even without dehumidification.
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We present an optimization strategy for atom-specific spin-polarization constants within the spin-polarized GFN2-xTB framework, aiming to enhance the accuracy of molecular simulations. We compare a sequential and global optimization of spin parameters for hydrogen, carbon, nitrogen, oxygen, and fluorine. Sensitivity analysis using Sobol indices guides the identification of the most influential parameters for a given reference dataset, allowing for a nuanced understanding of their impact on diverse molecular properties. In the case of the W4-11 dataset, substantial error reduction was achieved, demonstrating the potential of the optimization. Transferability of the optimized spin-polarization constants over different properties, however, is limited, as we demonstrate by applying the optimized parameters on a set of singlet-triplet gaps in carbenes. Further studies on ionization potentials and electron affinities highlight some inherent limitations of current extended tight-binding methods that can not be resolved by simple parameter optimization. We conclude that the significantly improved accuracy strongly encourages the present re-optimization of the spin-polarization constants, whereas the limited transferability motivates a property-specific optimization strategy.
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A detailed chemical understanding of H2 interactions with binding sites in the nanoporous crystalline structure of metal-organic frameworks (MOFs) can lay a sound basis for the design of new sorbent materials. Computational quantum chemical calculations can aid in this quest. To set the stage, we review general thermodynamic considerations that control the usable storage capacity of a sorbent. We then discuss cluster modeling of H2 ligation at MOF binding sites using state-of-the-art density functional theory (DFT) calculations, and how the binding can be understood using energy decomposition analysis (EDA). Employing these tools, we illustrate the connections between the character of the MOF binding site and the associated adsorption thermodynamics using four experimentally characterized MOFs, highlighting the role of open metal sites (OMSs) in accessing binding strengths relevant to room temperature storage. The sorbents are MOF-5, with no open metal sites, Ni2(m-dobdc), containing Lewis acidic Ni(II) sites, Cu(I)-MFU-4l, containing π basic Cu(I) sites and V2Cl2.8(btdd), also containing π-basic V(II) sites. We next explore the potential for binding multiple H2 molecules at a single metal site, with thermodynamics useful for storage at ambient temperature; a materials design goal which has not yet been experimentally demonstrated. Computations on Ca2+ or Mg2+ bound to catecholate or Ca2+ bound to porphyrin show the potential for binding up to 4 H2; there is precedent for the inclusion of both catecholate and porphyrin motifs in MOFs. Turning to transition metals, we discuss the prediction that two H2 molecules can bind at V(II)-MFU-4l, a material that has been synthesized with solvent coordinated to the V(II) site. Additional calculations demonstrate binding three equivalents of hydrogen per OMS in Sc(I) or Ti(I)-exchanged MFU-4l. Overall, the results suggest promising prospects for experimentally realizing higher capacity hydrogen storage MOFs, if nontrivial synthetic and desolvation challenges can be overcome. Coupled with the unbounded chemical diversity of MOFs, there is ample scope for additional exploration and discovery.
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In this article, we introduce the occupied-virtual orbitals for chemical valence (OVOCV). The OVOCVs can replace or complement the closely related idea of the natural orbitals for chemical valence (NOCV). The input is a difference density matrix connecting any initial single determinant to any final determinant, at a given molecular geometry, and a given one-particle basis. This arises in problems such as orbital rearrangement or charge transfer (CT) in energy decomposition analysis (EDA). The OVOCVs block-diagonalize the density difference operator into 2 × 2 blocks, which are spanned by one level that is filled in the initial state (the occupied OVOCV) and one that is empty (the virtual OVOCV). By contrast, the NOCVs fully diagonalize the density difference matrix and therefore are orbitals with mixed occupied-virtual character. Use of the OVOCVs makes it much easier to identify the donor and acceptor orbitals. We also introduce two different types of EDA methods with the OVOCVs and, most importantly, a charge decomposition analysis method that fixes the unreasonably large CT amount obtained directly from NOCV analysis. The square of the CT amount associated with each NOCV pair emerges as the appropriate value from the OVOCV analysis. When connecting the same initial and final states, this value is identical to the CT amount obtained from the independent absolutely localized molecular orbital (ALMO) complementary occupied-virtual orbital pair (COVP) analysis. The total, summed over all pairs, is also exactly the same as the independently suggested excitation number, as proved herein. Several examples are presented to compare NOCVs and OVOCVs: stretched H2+, a strong halogen bond between tetramethylthiourea and iodine, coordination of ethene in Zeise's salt, and binding in the Cp3La···C≡NCy complex.
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The double layer at the solid/electrolyte interface is a key concept in electrochemistry. Here, we present an experimental study combined with simulations, which provides a molecular picture of the double-layer formation under applied voltage. By THz spectroscopy we are able to follow the stripping away of the cation/anion hydration shells for an NaCl electrolyte at the Au surface when decreasing/increasing the bias potential. While Na+ is attracted toward the electrode at the smallest applied negative potentials, stripping of the Cl- hydration shell is observed only at higher potential values. These phenomena are directly measured by THz spectroscopy with ultrabright synchrotron light as a source and rationalized by accompanying molecular dynamics simulations and electronic-structure calculations.
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Accurate potential energy models of proteins must describe the many different types of noncovalent interactions that contribute to a protein's stability and structure. Pi-pi contacts are ubiquitous structural motifs in all proteins, occurring between aromatic and nonaromatic residues and play a nontrivial role in protein folding and in the formation of biomolecular condensates. Guided by a geometric criterion for isolating pi-pi contacts from classical molecular dynamics simulations of proteins, we use quantum mechanical energy decomposition analysis to determine the molecular interactions that stabilize different pi-pi contact motifs. We find that neutral pi-pi interactions in proteins are dominated by Pauli repulsion and London dispersion rather than repulsive quadrupole electrostatics, which is central to the textbook Hunter-Sanders model. This results in a notable lack of variability in the interaction profiles of neutral pi-pi contacts even with extreme changes in the dielectric medium, explaining the prevalence of pi-stacked arrangements in and between proteins. We also find interactions involving pi-containing anions and cations to be extremely malleable, interacting like neutral pi-pi contacts in polar media and like typical ion-pi interactions in nonpolar environments. Like-charged pairs such as arginine-arginine contacts are particularly sensitive to the polarity of their immediate surroundings and exhibit canonical pi-pi stacking behavior only if the interaction is mediated by environmental effects, such as aqueous solvation.
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Redox flow batteries (RFBs) are a promising stationary energy storage technology for leveling power supply from intermittent renewable energy sources with demand. A central objective for the development of practical, scalable RFBs is to identify affordable and high-performance redox-active molecules as storage materials. Herein, we report the design, synthesis, and evaluation of a new organic scaffold, indolo[2,3-b]quinoxaline, for highly stable, low-reduction potential, and high-solubility anolytes for nonaqueous redox flow batteries (NARFBs). The mixture of 2- and 3-(tert-butyl)-6-(2-methoxyethyl)-6H-indolo[2,3-b]quinoxaline exhibits a low reduction potential (-2.01 V vs Fc/Fc+), high solubility (>2.7 M in acetonitrile), and remarkable stability (99.86% capacity retention over 49.5 h (202 cycles) of H-cell cycling). This anolyte was paired with N-(2-(2-methoxyethoxy)-ethyl)phenothiazine (MEEPT) to achieve a 2.3 V all-organic NARFB exhibiting 95.8% capacity retention over 75.1 h (120 cycles) of cycling.
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The discovery that the commercial rubber antidegradant 6PPD reacts with ozone (O3) to produce a highly toxic quinone (6PPDQ) spurred a significant research effort into nontoxic alternatives. This work has been hampered by lack of a detailed understanding of the mechanism of protection that 6PPD affords rubber compounds against ozone. Herein, we report high-level density functional theory studies into early steps of rubber and PPD (p-phenylenediamine) ozonation, identifying key steps that contribute to the antiozonant activity of PPDs. In this, we establish that our density functional theory approach can achieve chemical accuracy for many ozonation reactions, which are notoriously difficult to model. Using adiabatic energy decomposition analysis, we examine and dispel the notion that one-electron charge transfer initiates ozonation in these systems, as is sometimes argued. Instead, we find direct interaction between O3 and the PPD aromatic ring is kinetically accessible and that this motif is more significant than interactions with PPD nitrogens. The former pathway results in a hydroxylated PPD intermediate, which reacts further with O3 to afford 6PPD hydroquinone and, ultimately, 6PPDQ. This mechanism directly links the toxicity of 6PPDQ to the antiozonant function of 6PPD. These results have significant implications for development of alternative antiozonants, which are discussed.
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Benzoquinonas , Fenilenodiaminas , Borracha , Poluentes Químicos da Água , Purificação da Água , Transporte de Elétrons , Ozônio/química , Borracha/química , Poluentes Químicos da Água/química , Purificação da Água/métodos , Fenilenodiaminas/química , Benzoquinonas/química , CinéticaRESUMO
Intersystem crossings between singlet and triplet states represent a crucial relaxation pathway in photochemical processes. Herein, we probe the intersystem crossing in hexafluoro-acetylacetone with ultrafast X-ray transient absorption spectroscopy at the carbon K-edge. We observe the excited state dynamics following excitation with 266 nm UV light to the 1ππ* (S2) state with element and site-specificity using a broadband soft X-ray pulse produced by high harmonic generation. These results are compared to X-ray spectra computed from orbital optimized density functional theory methods. It is found that the electron-withdrawing fluorine atoms decongest the X-ray absorption spectrum by enhancing separation between features originating from different carbon atoms. This facilitates the elucidation of structural and electronic dynamics at the chromophore. The evolution of the core-to-valence resonances at the carbon K-edge reveals an ultrafast population transfer between the 1nπ* (S1) and 3ππ* (T1) states on a 1.6 ± 0.4 ps time scale, which is similar to the 1.5 ps time scale earlier observed for acetylacetone [ J. Am. Chem. Soc. 2017, 139, 16576-16583, DOI: 10.1021/jacs.7b07532]. It therefore appears that terminal fluorination has little influence on the intersystem crossing rate of the acetylacetone chromophore. In addition, the significant role of hydrogen-bond opened and twisted rotational isomers is elucidated in the excited state dynamics by comparison of the experimental transient X-ray spectra with theory.
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Computational quantum chemistry can be more than just numerical experiments when methods are specifically adapted to investigate chemical concepts. One important example is the development of energy decomposition analysis (EDA) to reveal the physical driving forces behind intermolecular interactions. In EDA, typically the interaction energy from a good-quality density functional theory (DFT) calculation is decomposed into multiple additive components that unveil permanent and induced electrostatics, Pauli repulsion, dispersion, and charge-transfer contributions to noncovalent interactions. Herein, we formulate, implement, and investigate decomposing the forces associated with intermolecular interactions into the same components. The resulting force decomposition analysis (FDA) is potentially useful as a complement to the EDA to understand chemistry, while also providing far more information than an EDA for data analysis purposes such as training physics-based force fields. We apply the FDA based on absolutely localized molecular orbitals (ALMOs) to analyze interactions of water with sodium and chloride ions as well as in the water dimer. We also analyze the forces responsible for geometric changes in carbon dioxide upon adsorption onto (and activation by) gold and silver anions. We also investigate how the force components of an EDA-based force field for water clusters, namely MB-UCB, compare to those from force decomposition analysis.
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The stability and distributions of small water clusters generated in a supersonic beam expansion are interrogated by tunable vacuum ultraviolet (VUV) radiation generated at a synchrotron. Time-of-flight mass spectrometry reveals enhanced population of various protonated water clusters (H+(H2O)n) based upon ionization energy and photoionization distance from source, suggesting there are "magic" numbers below the traditional n = 21 that predominates in the literature. These intensity distributions suggest that VUV threshold photoionization (11.0-11.5 eV) of neutral water clusters close to the nozzle exit leads to a different nonequilibrium state compared to a skimmed molecular beam. This results in the appearance of a new magic number at 14. Metadynamics conformer searches coupled with modern density functional calculations are used to identify the global minimum energy structures of protonated water clusters between n = 2 and 21, as well as the manifold of low-lying metastable minima. New lowest energy structures are reported for the cases of n = 5, 6, 11, 12, 16, and 18, and special stability is identified by several measures. These theoretical results are in agreement with the experiments performed in this work in that n = 14 is shown to exhibit additional stability, based on the computed second-order stabilization energy relative to most cluster sizes, though not to the extent of the well-known n = 21 cluster. Other cluster sizes that show some additional energetic stability are n = 7, 9, 12, 17, and 19. To gain insight into the balance between ion-water and water-water interactions as a function of the cluster size, an analysis of the effective two-body interactions (which sum exactly to the total interaction energy) was performed. This analysis reveals a crossover as a function of cluster size between a water-hydronium-dominated regime for small clusters and a water-water-dominated regime for larger clusters around n = 17.
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In typical carbonyl-containing molecules, bond dissociation events follow initial excitation to nπCâO* states. However, in acetyl iodide, the iodine atom gives rise to electronic states with mixed nπCâO* and nσC-I* character, leading to complex excited-state dynamics, ultimately resulting in dissociation. Using ultrafast extreme ultraviolet (XUV) transient absorption spectroscopy and quantum chemical calculations, we present an investigation of the primary photodissociation dynamics of acetyl iodide via time-resolved spectroscopy of core-to-valence transitions of the I atom after 266 nm excitation. The probed I 4d-to-valence transitions show features that evolve on sub-100-fs time scales, reporting on excited-state wavepacket evolution during dissociation. These features subsequently evolve to yield spectral signatures corresponding to free iodine atoms in their spin-orbit ground and excited states with a branching ratio of 1.1:1 following dissociation of the C-I bond. Calculations of the valence excitation spectrum via equation-of-motion coupled cluster with single and double substitutions (EOM-CCSD) show that initial excited states are of spin-mixed character. From the initially pumped spin-mixed state, we use a combination of time-dependent density functional theory (TDDFT)-driven nonadiabatic ab initio molecular dynamics and EOM-CCSD calculations of the N4,5 edge to reveal a sharp inflection point in the transient XUV signal that corresponds to rapid C-I homolysis. By examining the molecular orbitals involved in the core-level excitations at and around this inflection point, we are able to piece together a detailed picture of C-I bond photolysis in which d â σ* transitions give way to d â p excitations as the bond dissociates. We also report theoretical predictions of short-lived, weak 4d â 5d transitions in acetyl iodide, validated by weak bleaching in the experimental transient XUV spectra. This joint experimental-theoretical effort has thus unraveled the detailed electronic structure and dynamics of a strongly spin-orbit coupled system.
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Second-order Møller-Plesset perturbation theory (MP2) often breaks down catastrophically in small-gap systems, leaving much to be desired in its performance for myriad chemical applications such as noncovalent interactions, thermochemistry, and dative bonding in transition metal complexes. This divergence problem has reignited interest in Brillouin-Wigner perturbation theory (BWPT), which is regular at all orders but lacks size consistency and extensivity, severely limiting its application to chemistry. In this work, we propose an alternative partitioning of the Hamiltonian that leads to a regular BWPT perturbation series that, through the second order, is size-extensive, size-consistent (provided its Hartree-Fock reference is also), and orbital invariant. Our second-order size-consistent Brillouin-Wigner (BW-s2) approach can describe the exact dissociation limit of H2 in a minimal basis set, regardless of the spin polarization of the reference orbitals. More broadly, we find that BW-s2 offers improvements relative to MP2 for covalent bond breaking, noncovalent interaction energies, and metal/organic reaction energies, although rivaling coupled-cluster with single and double substitutions for thermochemical properties.
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Utilizing localized orbitals, local correlation theory can reduce the unphysically high system-size scaling of post-Hartree-Fock (post-HF) methods to linear scaling in insulating molecules. The sparsity of the four-index electron repulsion integral (ERI) tensor is central to achieving this reduction. For second-order Møller-Plesset theory (MP2), one of the simplest post-HF methods, only the (ia|jb) ERIs are needed, coupling occupied orbitals i, j and virtuals a, b. In this paper, we compare the numerical sparsity (called the "ragged list") and two other approaches revealing the low-rank sparsity of the ERI. The ragged list requires only one set of (localized) virtual orbitals, and we find that the orthogonal valence virtual-hard virtual set of virtuals originally proposed by Subotnik et al. gives the sparsest ERI tensor. To further compress the ERI tensor, the pair natural orbital (PNO) type representation uses different sets of virtual orbitals for different occupied orbital pairs, while the occupied-specific virtual (OSV) approach uses different virtuals for each occupied orbital. Our results indicate that while the low-rank PNO representation achieves significant rank reduction, it also requires more memory than the ragged list. The OSV approach requires similar memory to that of the ragged list, but it involves greater algorithmic complexity. An approximation (called the "fixed sparsity pattern") for solving the local MP2 equations using the numerically sparse ERI tensor is proposed and tested to be sufficiently accurate and to have highly controllable error. A low-scaling local MP2 algorithm based on the ragged list and the fixed sparsity pattern is therefore promising.
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Despite its simplicity and relatively low computational cost, second-order Møller-Plesset perturbation theory (MP2) is well-known to overbind noncovalent interactions between polarizable monomers and some organometallic bonds. In such situations, the pairwise-additive correlation energy expression in MP2 is inadequate. Although energy-gap dependent amplitude regularization can substantially improve the accuracy of conventional MP2 in these regimes, the same regularization parameter worsens the accuracy for small molecule thermochemistry and density-dependent properties. Recently, we proposed a repartitioning of Brillouin-Wigner perturbation theory that is size-consistent to second order (BW-s2), and a free parameter (α) was set to recover the exact dissociation limit of H2 in a minimal basis set. Alternatively α can be viewed as a regularization parameter, where each value of α represents a valid variant of BW-s2, which we denote as BW-s2(α). In this work, we semi-empirically optimize α for noncovalent interactions, thermochemistry, alkane conformational energies, electronic response properties, and transition metal datasets, leading to improvements in accuracy relative to the ab initio parameterization of BW-s2 and MP2. We demonstrate that the optimal α parameter (α = 4) is more transferable across chemical problems than energy-gap-dependent regularization parameters. This is attributable to the fact that the BW-s2(α) regularization strength depends on all of the information encoded in the t amplitudes rather than just orbital energy differences. While the computational scaling of BW-s2(α) is iterative O(N5), this effective and transferable approach to amplitude regularization is a promising route to incorporate higher-order correlation effects at second-order cost.
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VV10 is a powerful nonlocal density functional for long-range correlation that is used to include dispersion effects in many modern density functionals, such as the meta-generalized gradient approximation (mGGA), B97M-V, the hybrid GGA, ωB97X-V, and the hybrid mGGA, ωB97M-V. While energies and analytical gradients for VV10 are already widely available, this study reports the first derivation and efficient implementation of the analytical second derivatives of the VV10 energy. The additional compute cost of the VV10 contributions to analytical frequencies is shown to be small in all but the smallest basis sets for recommended grid sizes. This study also reports the assessment of VV10-containing functionals for predicting harmonic frequencies using the analytical second derivative code. The contribution of VV10 to simulating harmonic frequencies is shown to be small for small molecules but important for systems where weak interactions are important, such as water clusters. In the latter cases, B97M-V, ωB97M-V, and ωB97X-V perform very well. The convergence of frequencies with respect to the grid size and atomic orbital basis set size is studied, and recommendations are reported. Finally, scaling factors to allow comparison of scaled harmonic frequencies with experimental fundamental frequencies and to predict zero-point vibrational energy are presented for some recently developed functionals (including r2SCAN, B97M-V, ωB97X-V, M06-SX, and ωB97M-V).